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Mixed Models for Longitudinal Continuous and Dichotomous Data
Donald Hedeker, Ph.D.

Practical Tools for Causal Inference
Joseph Schafer, Ph.D.

The Methodology Center held its 12th Summer Institute on Longitudinal Methods June 4-6, 2007. The Institute, sponsored by The Pennsylvania State University and the National Institute on Drug Abuse, provided researchers who had varying levels of methodological training the opportunity to familiarize themselves with longitudinal data analysis. In addition, the institute was designed to facilitate the exchange of ideas among substantive and methodological researchers. This year's three-day Institute featured sessions by both Donald Hedeker and Joseph Schafer.

Mixed Models for Longitudinal Continuous and Dichotomous Data
In Dr. Hedeker’s session, attendees learned about the use of mixed models for analysis of longitudinal, or repeated measures, data. The focus was on application of these models, with direct application illustrated using standard statistical software (i.e., SAS). Some of the topics covered included: (1) mixed models for continuous normal outcomes, (2) mixed pattern-mixture and selection models for missing data, and (3) mixed models for dichotomous outcomes.
  • The basic mixed-effects regression model was introduced and described, including use of polynomials for expressing change across time, the multilevel representation of the mixed model, treatment of time-invariant and time-varying covariates, and modeling of the variance-covariance structure of the repeated measures. Some aspects of model estimation and inference were reviewed.
  • Mixed models allow incomplete data across time and assume that these missing observations are "missing at random" (MAR) under maximum likelihood estimation. Approaches that can go further, and don't necessarily assume MAR, are through the use of pattern mixture and selection models. Applications were described of mixed pattern mixture and selection models, including illustrations of how to estimate such models using standard software.
  • Since dichotomous outcomes are common in many areas of research, mixed models for longitudinal dichotomous data are important. In particular, mixed logistic regression models were presented and described. Attention was paid to the "subject-specific" interpretation of the parameters in these models, as well as techniques for deriving "population averaged" estimates.

Practical Tools for Causal Inference
In Dr. Schafer’s session, attendees reviewed key concepts of causal inference under the framework known as Rubin’s causal model. Participants came to understand the meaning of an average causal effect (ACE) and how it differs from a regression coefficient. We learned about the various methods for estimating ACEs. We also extended the notion of an ACE to causal regression and multilevel models.

"Association is not causation." Well designed randomized experiments remain the gold standard for drawing causal conclusions, but random assignment is not always tenable. Social and behavioral scientists need practical tools for estimating causal effects from observational data. They also need to understand the strengths and limitations of these methods (e.g., to realize when causal inference should not even be attempted).

This session did not involve hands-on computing. All techniques for estimating ACE's and computing standard errors, however, were illustrated with sample SAS/R code and worked examples.


Donald Hedeker, Ph.D. is a Professor of Biostatistics in the School of Public at the University of Illinois at Chicago. He received his Ph.D. in Quantitative Psychology from The University of Chicago in 1989. Don's main expertise is in the development and use of statistical methods for clustered and longitudinal data, with particular emphasis on mixed-effects models. He is the primary author of several freeware computer programs for mixed-effects analysis. In 2000, Don was named a Fellow of the American Statistical Association.

Joseph Schafer, Ph.D. is an Associate Professor of Statistics and a scientist in the Methodology Center at the Pennsylvania State University. He received his Ph.D. in Statistics from Harvard University in 1992. Joe has done extensive research on methods for handling missing data, and also has expertise in causal inference, as well as latent class and latent transition analysis. Joe has released several freeware computer programs for multiple imputation, and authored the well-cited book Analysis of Incomplete Multivariate Data.


Comments about the Summer Institute

Not only is Penn State’s Methodology Center considered one of the best statistical training centers in the country, but the center is funded by the National Institute on Drug Abuse—because of this, they can attract well-known speakers who are leaders in substance-use research. This provides a great environment in which we can learn and network.
Michael Marshal, Assistant Professor of Psychiatry at the University of Pittsburgh
Summer Institute Improves Research Skills by Liam Jackson

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